The two triangles given are similar. Find the values of x and y when the smaller triangle has an area of 45 cm squared.

x
y
135 cm
30 cm
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Part 1
The value of x is
  
3 StartRoot 5 EndRoot cm and the value of y is
  
enter your response here cm.
​(Type exact​ answers, using radicals as needed. Rationalize all​ denominators.)

1 answer

The ratio of the two triangles' corresponding sides is equal to the square root of the ratio of their areas.

Let x be the height of the smaller triangle. The area of the smaller triangle is given by (1/2)*x*y/2 = 45 cm^2.

Therefore, x*y = 90.

Since the two triangles are similar, the ratio of their corresponding sides is the same:

x/135 = y/30

Solving these two equations simultaneously, we get:

x = 18√5 cm and y = 4√5 cm

So, the values of x and y are 18√5 cm and 4√5 cm respectively.